Nonlinear static analysis of plates with arbitrary aspect ratios using Extended Higher Order Sandwich Panel Theory

Abstract

A nonlinear static analysis of the sandwich plate using variational techniques and the Ritz method is presented. The kinematic description developed for a sandwich plate undergoing small strains and moderate rotations within the framework of Extended Higher Order Sandwich Panel Theory is considered. Employing the Ritz method, the total potential energy of the system is developed. Four different cases and combinations of boundary conditions are studied and assumed solutions satisfying the geometric boundary conditions are developed. The total potential energy results in nonlinear algebraic equations for the unknown coefficients in the assumed solution. The nonlinear equations are then solved using the Newton–Raphson method. A convergence study is then carried out to study the effect of variation of the number of terms in the assumed solution. In order to analyze the effect of inclusion of nonlinear effects in the core, results are computed considering only the facesheets with nonlinear strains and the core is considered to remain in the linear range. A stress analysis is carried out to compare the stresses predicted by the linear theory against the nonlinear results. After calculating and comparing the results for the simply supported case, three more cases for different sets of boundary conditions are also considered and presented. Since EHSAPT allows for analysis of plates with variable aspect ratios a further case where it is assumed that the depth of the plate is half the width is also considered and the results are presented for various geometric configurations.